| Exam Board | SPS |
|---|---|
| Module | SPS SM Mechanics (SPS SM Mechanics) |
| Year | 2023 |
| Session | January |
| Marks | 5 |
| Topic | Forces, equilibrium and resultants |
| Type | Particle suspended by strings |
| Difficulty | Standard +0.3 This is a straightforward statics problem requiring resolution of forces in equilibrium. Part (i) uses Pythagoras theorem (since forces are perpendicular) to find the unknown tension. Part (ii) requires recognizing that vertical equilibrium demands an upward component, which horizontal strings cannot provide. Both parts are standard textbook exercises with no novel problem-solving required. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.04b Equilibrium: zero resultant moment and force |
\begin{enumerate}
\item A parcel $P$ of weight 50 N is being held in equilibrium by two light, inextensible strings $A P$ and $B P$. The string $A P$ is attached to a wall at $A$, and string $B P$ passes over a smooth pulley which is at the same height as $A$, as shown in the diagram.
\end{enumerate}
When the tension in $B P$ is 40 N , the strings are at right angles to each other.\\
\includegraphics[max width=\textwidth, alt={}, center]{4109fba0-077e-472b-b37f-7ac2e45aacc7-08_531_768_479_699}\\
(i) Find the tension in string $A P$.\\
(ii) Explain why the parcel can never be in equilibrium, with both strings horizontal.
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\hfill \mbox{\textit{SPS SPS SM Mechanics 2023 Q3 [5]}}